Analogues of IBN and related properties for modules.
type: Item
instance of: scholarly article
title: Analogues of IBN and related properties for modules.
zbMATH Open document ID: 1169.16002
author: K. Varadarajan
published in: Acta Mathematica Hungarica
publication date: 2008-10-21T00:00:00Z
review text: The author introduces and studies module-theoretic versions of several ring properties, namely, invariant basis number, rank condition, stable finiteness and strong rank condition. The corresponding module properties are called, respectively, unique exponent property, exponent condition, stable finiteness and strong exponent condition. The first three of them hold for a module \(M\) if and only if the corresponding ring property holds for the ring \(\text{End}(M)\) but, while the strong rank condition for \(\text{End}(M)\) implies that \(M\) satisfies the strong exponent condition, the converse is not true in general as shown by an example given at the end of the paper. The author studies the effect on each of these properties of standard module-theoretic operations and also the behavior of the discussed properties under change of rings or passing to modules of polynomials or power series. The paper is well written and contains several examples that illustrate the theory.
Mathematics Subject Classification ID: 16D10
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16D80
Mathematics Subject Classification ID: 16P70
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16U20
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 16W60
zbMATH DE Number: 5355121
zbMATH Keywords: invariant basis number
zbMATH Keywords: rank conditions
zbMATH Keywords: stable finiteness
zbMATH Keywords: strong rank condition
zbMATH Keywords: classes of modules
zbMATH Keywords: unique exponent property
zbMATH Keywords: exponent condition
zbMATH Keywords: polynomial rings
zbMATH Keywords: power series rings
zbMATH Keywords: inverse polynomials
reviewed by: José L. Gómez-Pardo
MaRDI profile type: Publication
full work available at URL: s10474-007-7008-3
OpenAlex ID: W2085735062
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DOI: 10.1007/S10474-007-7008-3
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description: scientific article; zbMATH DE number 5355121